Mechanism Of Wave-induced Fluid Flow Research Articles

Frequency-dependent elastic properties of fracture-induced VTI rocks in a fluid-saturated porous and microcracked background

Fractures are widely distributed underground. The stiffness matrix of fractured rocks has been extensively investigated in a fluid-saturated porous background medium. However, the existing stiffness models only incorporate the attenuation mechanism of wave-induced fluid flow (WIFF). For macroscopic fractures, the elastic scattering (ES) of fractures cannot be ignored. To alleviate this issue, a frequency-dependent stiffness matrix model is developed, including the mesoscopic WIFF between fractures and background (FB-WIFF), the microscopic squirt flow, and the macroscopic ES from the fractures. By combining the far-field scattered wavefields of normal incident P and SV waves with the linear slip theory, the dynamic full-stiffness matrices for fracture-induced effective vertically transversely isotropic rocks in a fluid-saturated porous and microcracked background are derived. Then, the P, SV, and SH-wave velocities and attenuation can be obtained through the Kelvin-Christoffel equation. The results indicate that the FB-WIFF mechanism significantly affects the velocities and attenuation of the P and SV waves but has almost no effect on the SH wave, whereas the squirt flow and ES mechanisms affect the velocities and attenuation of all the P, SV, and SH waves. For validation, the model is compared with existing models and previous experimental ultrasonic data.

Dual attenuation peaks revealing mesoscopic and microscopic fluid flow in partially oil-saturated Fontainebleau sandstones

SUMMARY We conducted stress–strain oscillation experiments on dry and partially oil-saturated Fontainebleau sandstone samples over the 1–2000 Hz band at different confining pressures to investigate the wave-induced fluid flow (WIFF) at mesoscopic and microscopic scales and their interaction. Three tested rock samples have similar porosity between 6 and 7 per cent and were partially saturated to different degrees with different oils. The measurement results exhibit a single or two attenuation peaks that are affected by the saturation degree, oil viscosity and confining pressure. One peak, exhibited by all samples, shifts to lower frequencies with increasing pressure, and is mainly attributed to grain contact- or microcrack-related squirt flow based on modelling of its characteristics and comparison with other experiment results for sandstones. The other peak is present at smaller frequencies and shifts to higher frequencies as the confining pressure increases, showing an opposite pressure dependence. This contrast is interpreted as the result of fluid flow patterns at different scales. We developed a dual-scale fluid flow model by incorporating the squirt flow effect into the patchy saturation model, which accounts for the interaction of WIFFs at microscopic and mesoscopic scales. This model provides a reasonable interpretation of the measurement results. Our broad-frequency-band measurements give physical evidence of WIFFs co-existing at two different scales, and combining with modelling results, it suggests that the WIFF mechanisms, related to pore microstructure and fluid distribution, interplay with each other and jointly control seismic attenuation and dispersion at reservoir conditions. These observations and modelling results are useful for quantitative seismic interpretation and reservoir characterization, specifically they have potential applications in time-lapse seismic analysis, fluid prediction and reservoir monitoring.

Fracture analysis on an infinite row of collinear permeable cracks in a porous medium

The dynamic (frequency-dependent) mode-I stress intensity factor (SIF) is obtained for a porous medium containing an array of equally distributed collinear cracks. Unlike previous work in which the cracks are assumed to be dry and impermeable, this paper studies the case that the crack is fluid-saturated and permeable. The cracks are under the action of a normal incidence of a time-harmonic plane longitudinal (P) wave. The interaction between the collinear cracks and the mechanism of wave-induced fluid flow (scattered slow P wave) can significantly affect the magnitude and frequency-dependent trend of the SIF, in particular at low frequencies. At low frequencies, the magnitude of the SIF increases monotonously with the decreasing distance between the adjacent cracks and can be much larger than that of a single crack, implying that the material strength can be greatly lowered by the interaction of cracks. However, at higher frequencies, the impacts of interacting cracks are negligible. The comparison with the counterpart of dry impermeable cracks reveals that the magnitude of SIF is lower than that of dry impermeable cracks owing to effective normal stress effect. Moreover, unlike the SIF of dry impermeable cracks for which a peak value is observed around elastic wave resonance frequency, the corresponding SIF of fluid-saturated permeable cracks monotonously decreases with the increasing frequency. This frequency-dependent trend is attributed to the conversion of incident energy into the slow P wave. The obtained results reveal significant influences of the presence of pore fluid and interaction of collinear cracks upon the SIF, both magnitudes and frequency-dependent trends. Such information is useful in predicting the fracture strength of saturated porous materials subjected to oscillating loads.

Pore fluid effects on S-wave attenuation caused by wave-induced fluid flow

We studied seismic attenuation of P- and S-waves caused by the physical mechanism of wave-induced fluid flow at the mesoscopic scale. Stress relaxation experiments were numerically simulated by solving Biot’s equations for consolidation of 2D poroelastic media with finite-element modeling. The experiments yielded time-dependent stress-strain relations that were used to calculate the complex moduli from which frequency-dependent attenuation was determined. Our model consisted of periodically distributed circular or elliptical heterogeneities with much lower porosity and permeability than the background media, which contained 80% of the total pore space of the media. This model can represent a hydrocarbon reservoir, where the porous background is fully saturated with oil or gas and the low-porosity regions are always saturated with water. Three different saturation scenarios were considered: oil-saturated (80% oil, 20% water), gas-saturated (80% gas, 20% water), and fully water-saturated media. Varying the dry bulk and shear moduli in the background and in the heterogeneities, a consistent tendency was observed in the relative behavior of the S-wave attenuation among the different saturation scenarios. First, in the gas-saturated media the S-wave attenuation was very low and much lower than in the oil-saturated or in the fully water-saturated media. Second, at low frequencies the S-wave attenuation was significantly higher in the oil-saturated media than in the fully water-saturated media. The P-wave attenuation exhibited a more variable relative behavior among the different saturation degrees. Based on the mechanism of wave-induced fluid flow and on our numerical results, we suggest that S-wave attenuation could be used as an indicator of fluid content in a reservoir. Additionally, we observed that impermeable barriers in the background can cause a significant increase in S-wave attenuation. This suggests that S-wave attenuation could also be an indicator of permeability changes in a reservoir due to, for example, fracturing operations.

Frequency-dependent attenuation as a potential indicator of oil saturation

At seismic frequencies, wave-induced fluid flow is a major cause of P-wave attenuation in partially saturated porous rocks. Attenuation is of great importance for the oil industry in the interpretation of seismic field data. Here, the effects on P-wave attenuation resulting from changes in oil saturation are studied for media with coexisting water, oil, and gas. For that, creep experiments are numerically simulated by solving Biot's equations for consolidation of poroelastic media with the finite-element method. The experiments yield time-dependent stress–strain relations that are used to calculate the complex P-wave modulus from which frequency-dependent P-wave attenuation is determined. The models are layered media with periodically alternating triplets of layers. Models consisting of triplets of layers having randomly varying layer thicknesses are also considered. The layers in each triplet are fully saturated with water, oil, and gas. The layer saturated with water has lower porosity and permeability than the layers saturated with oil and gas. These models represent hydrocarbon reservoirs in which water is the wetting fluid preferentially saturating regions of lower porosity. The results from the numerical experiments showed that increasing oil saturation, connected to a decrease in gas saturation, resulted in a significant increase of attenuation at low frequencies (lower than 2 Hz). Furthermore, replacing the oil with water resulted in a distinguishable behavior of the frequency-dependent attenuation. These results imply that, according to the physical mechanism of wave-induced fluid flow, frequency-dependent attenuation in media saturated with water, oil, and gas is a potential indicator of oil saturation. ► Attenuation due to interlayer flow is numerically studied using quasi-static tests. ► Media partially saturated with water, gas, and oil are considered. ► At low seismic frequencies, attenuation increases with increasing oil saturation. ► Increasing oil or water saturations result in distinguishable attenuation behaviors. ► Frequency-dependent attenuation is a potential indicator of oil saturation.

Poroelastic analysis of permeability effects in thinly layered porous media

The mechanism of wave-induced fluid flow, which causes significant attenuation and dispersion of seismic waves in heterogeneous porous media, opens a potential opportunity to estimate fluid-mobility properties from seismic data. However, the permeability effects on seismic data vary for different reservoir environments, so rules of thumb are difficult to establish. Two types of reservoir models were selected. One represents shallow, unconsolidated, low-impedance reservoirs. The other represents deep, consolidated, high-impedance reservoirs. Using analytic equations and wave-propagation numerical studies, permeability effects were investigated on the magnitude and phase of normal-incident reflection coefficients from an interface between an upper nondispersive medium and a lower thinly layered porous medium. The study found that permeability can affect reflection amplitudes significantly. For high-impedance reservoirs, magnitude of the reflection coefficient decreases when permeability increases. However, for low-impedance reservoirs, reflection magnitude increases as permeability increases.

Dynamic permeability of porous rocks and its seismic signatures

In inhomogeneous porous media, the mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection with this phenomenon, we study the impact of spatial permeability fluctuations on the dynamic behavior of porous materials. This heterogeneous permeability distribution further complicates the ongoing efforts to extract flow permeability from seismic data. Based on the method of statistical smoothing applied to Biot’s equations of poroelasticity, we derive models for the dynamic-equivalent permeability in 1D and 3D randomly inhomogeneous media. The low-frequency limit of this permeability corresponds to the flow permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation and dispersion of P-waves, also obtained by the method of smoothing. The resulting attenuation and dispersion model is confirmed by numerical computations in randomly layered poroelastic structures. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. The peak attenuation shifts along the frequency axis depending on the strength of the permeability fluctuations. We conclude that estimation of flow permeability from seismic attenuation is only possible if permeability fluctuations are properly accounted for.